We study nonlinear electronic transport symmetries in Aharonov-Bohm interferometers subjected to inelastic-scattering effects and show that odd (even) conductance terms are even (odd) in the magnetic field when the junction is (left-right) spatially symmetric. This observation does not hold when spatial inversion symmetry is broken, as we show numerically. Under elastic dephasing effects, the Onsager-Casimir symmetry is maintained beyond linear response, irrespective of spatial asymmetries.